burgers_2012_ornl

burgers_2012_ornl, "Parallel Collocation for Uncertainty Quantification on High Performance Systems", a talk at Oak Ridge National Laboratory on 2 May 2012, part of the SAMSI workshop "Uncertainty Quantification for High-Performance Computing".

• burgers_2012_ornl.tex
• burgers_2012_ornl.pdf

The following files were used:

• burgers_base.png, the "base" solution of the steady Burgers equation.
• burgers_convergence.png, study of the approximation of the quantity of interest, Q=U(X=0,T=3), for the time dependent Burgers equation, using sparse grids and the Monte Carlo method, for three values of viscosity.
• burgers_grid.png, a schematic of the time and space grid for Burgers equation with an initial condition and periodic boundaries.
• burgers_ic.png, a plot suggestion how an initial condition for the time dependent Burgers equation could be defined by 9 data values and a spline.
• burgers_ic_perturb.png, a plot showing how the solution profile at time = 3 of the Burgers equation would be affected by changing any one of the 9 data values that define the initial condition.
• burgers_shock.png, a 3D plot showing how the inviscid Burgers equation can develop a shock, causing the solution process to break down.
• burgers_time2.png, the "base" solution of the time dependent Burgers equation, at T = 2.
• burgers_time3.png, the "base" solution of the time dependent Burgers equation, at T = 3.
• cc_3d.png, images of the first 6 sparse grids in 3D, based on the Clenshaw Curtis points.
• fsu_logo.pdf, a logo for FSU.
• sensitivity_a.png, a rough exploration of the sensitivity of the "base" solution of the steady Burgers equation with respect to the location of the left boundary condition.
• sensitivity_alpha.png, a rough exploration of the sensitivity of the "base" solution of the steady Burgers equation with respect to the value of the left boundary condition.
• sensitivity_nu.png, a rough exploration of the sensitivity of the "base" solution of the steady Burgers equation with respect to the viscosity.
• tanh_plot.png, a plot of the hyperbolic tangent function, which is essentially the solution to our simple steady Burgers equation.
• x0_alpha.png, a plot of the location where the solution to the steady Burgers equation changes sign, as a function of the value of alpha, the value specified at the left boundary.